Research-based Modular Curriculum for Developing Mathematical Tools for Upper-Division Physics

As part of a larger project that attends to investigating the gap between mathematics that is taught in math courses and the mathematics used in upper-division physics courses, we present curriculum on Separation of Variables and Taylor Series. In both tutorials, students work through mathematics using physics examples, but they are intended to not rely heavily on the physics content. This is intended to alleviate the need to get caught up on physics concepts so that students can gain experience and focus on the mathematics at play. The tutorials use examples from Quantum Mechanics, Electricity and Magnetism, and Junior-level mechanics, and, as such, could be used in any of these courses as well as a Math Methods course. The curriculum is designed in a modular fashion so that one could start with an example problem from E&M and then move to Quantum Mechanics and vice versa. The tutorials have been vetted by experts in mathematics and physics faculty, via one-on-one interviews with students, as well as videoed classroom usage.